展開する ((c+x)^2)/(c^2x^2)

解

展開する

\frac{( c + x ) ^{2}}{c ^{2} x ^{2}}

\frac{1}{x ^{2}} + \frac{2}{c x} + \frac{1}{c ^{2}}

解答ステップ

\frac{( c + x ) ^{2}}{c ^{2} x ^{2}}

(c + x)^{2} = c^{2} + 2 c x + x^{2}

= \frac{c ^{2} + 2 c x + x ^{2}}{c ^{2} x ^{2}}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{c ^{2} + 2 c x + x ^{2}}{c ^{2} x ^{2}} = \frac{c ^{2}}{c ^{2} x ^{2}} + \frac{2 c x}{c ^{2} x ^{2}} + \frac{x ^{2}}{c ^{2} x ^{2}}

= \frac{c ^{2}}{c ^{2} x ^{2}} + \frac{2 c x}{c ^{2} x ^{2}} + \frac{x ^{2}}{c ^{2} x ^{2}}

キャンセル

\frac{c ^{2}}{c ^{2} x ^{2}} : \frac{1}{x ^{2}}

= \frac{1}{x ^{2}} + \frac{2 c x}{c ^{2} x ^{2}} + \frac{x ^{2}}{c ^{2} x ^{2}}

キャンセル

\frac{2 c x}{c ^{2} x ^{2}} : \frac{2}{c x}

= \frac{1}{x ^{2}} + \frac{2}{c x} + \frac{x ^{2}}{c ^{2} x ^{2}}

キャンセル

\frac{x ^{2}}{c ^{2} x ^{2}} : \frac{1}{c ^{2}}

= \frac{1}{x ^{2}} + \frac{2}{c x} + \frac{1}{c ^{2}}